
The dimensional formula for electric flux is
A.
B.
C.
D.
Answer
487.5k+ views
Hint: The dimensional formula is defined as the expression for the unit of a physical quantity in terms of fundamental quantities that are mass ( ), length ( ), and time ( ). Here, we will use the formula of force to find the value of the electric field. Then, we will use the formula of electric flux to calculate the dimensional formula of the electric flux.
Formula used:
The formula for force is given by
Where is the force, is the charge and is the electric field.
Also, the formula for the electric flux is given by
Here, is the electric flux, is the electric field and is the surface area.
Complete step by step answer:
Now, the electric flux can be defined as the measure of the electric field that passes through a given surface area. Also, the electric flux can be defined product of the electric field and the area of the surface, which is shown below
Electric flux
Here, represents the magnitude of the electric field, represents the area of the surface, and represents the angle between the electric field vector and the area vector .
Now, the formula of the force is given by
Therefore, we can calculate the electric field from the above equation as
Therefore, putting this value in the electric flux, we get
Electric flux
Now, as we know that the S.I. unit of the electric field is
Therefore the dimensional formula can be calculated as shown below
Now, is the unit of mass, is the unit of length, is the unit of time, and is the unit of the current. Therefore, the dimensional formula of the electric flux density is .
So, the correct answer is “Option D”.
Note:
An alternate method to calculate the dimensional formula of electric flux is by using Gauss’s law.
The electric flux according to Gauss’s law through a closed surface is shown below
Now, the dimensional formula for the charge,
Also, the dimensional formula for the permittivity,
Therefore, the dimensional formula of electric flux is given by putting the dimensional formula of both the quantities as shown below
Which is the required dimensional formula.
Formula used:
The formula for force is given by
Where
Also, the formula for the electric flux is given by
Here,
Complete step by step answer:
Now, the electric flux can be defined as the measure of the electric field that passes through a given surface area. Also, the electric flux can be defined product of the electric field and the area of the surface, which is shown below
Electric flux
Here,
Now, the formula of the force is given by
Therefore, we can calculate the electric field from the above equation as
Therefore, putting this value in the electric flux, we get
Electric flux
Now, as we know that the S.I. unit of the electric field is
Therefore the dimensional formula can be calculated as shown below
Now,
So, the correct answer is “Option D”.
Note:
An alternate method to calculate the dimensional formula of electric flux is by using Gauss’s law.
The electric flux according to Gauss’s law through a closed surface is shown below
Now, the dimensional formula for the charge,
Also, the dimensional formula for the permittivity,
Therefore, the dimensional formula of electric flux is given by putting the dimensional formula of both the quantities as shown below
Which is the required dimensional formula.
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